You could create a separate DataLoader for each run, each with a unique name. The outputs would then be separated. I am not currently aware of way to do this by just specifying the path to where to save.
Thank you for your reply and for the ticket reference.
Indeed, this is exactly the same issue. I see that this ticket has been open since 2017 - any chance that this can be resolved soon? Unfortunately, I do not see a way for me to comment directly in the ticket.